Harmonic analysis on homogeneous spaces

Description

The intent of this book is to give students of mathematics and mathematicians in diverse fields an entry into the subject of harmonic analysis on homogeneous spaces. It is hoped that the book could be used as a supplement to a standard one-year course in Lie groups and Lie algebras or as the main text in a more unorthodox course on the subject. Pains have been taken to build the subject matter gradually from fairly easy material to the more advanced material. Exercises have been included at the end of each chapter to help the reader's comprehension of the material. We have also adopted a decimal system of labeling statements, lemmas,theorems, etc. (For example, 3.7.2(1) means the first displayed formula or assertion in the second paragraph of the seventh section of Chapter 3.) We felt after much soul-searching that this system of presentation would in the long-run make the book more accessible since it simplifies the cross-referencing. However, once one decides to consistently use a system of labeling such as ours, one is forced to write the material of the book in a "quantized" form. The writing also becomes dry and discussions of material are hard to fit into the text. It is hoped that the underlying mathematics will motivate the reader to tolerate the exposition. To somewhat temper the dryness of exposition,each chapter has an introduction which will, hopefully, help the reader to organize and motivate the material of the chapter.